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How do you evaluate the integral $$\int \frac{dz}{15 + 2z -z^2}$$ and $$\int ^\frac{\pi}{3} _0 \frac{\sec\theta \tan \theta}{ \sqrt {e^{\sec\theta}}}d\theta?$$

I had a book that discusses these, but from what I read, it didn't apply to these integrals. How do you evaluate these integrals?

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    $\begingroup$ what did you try? And it is better to devide integrals like one per-topic. For example the first one can be taken completeing the square $\endgroup$
    – M.Mass
    Aug 6 '17 at 16:16
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For the first integral, write $$\int \frac{dz}{15 + 2z -z^2} =\int \frac{dz}{(5-z)(3+z)} = \int \frac{A}{5-z}dz + \int \frac{B}{3+z} dz $$ and then find $A$ and $B$. Then integrate each one separately.

For the second one, do a $u$-substitution: let $u=\sec \theta$. Then $du =\sec \theta\tan \theta \:d\theta$.

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